Search the forum,

excellent

In commutative algebra, a quasi-excellent ring is a Noetherian commutative ring that behaves well with respect to the operation of completion, and is called an excellent ring if it is also universally catenary. Excellent rings are one answer to the problem of finding a natural class of "well-behaved" rings containing most of the rings that occur in number theory and algebraic geometry. At one time it seemed that the class of Noetherian rings might be an answer to this problem, but Masayoshi Nagata and others found several strange counterexamples showing that in general Noetherian rings need not be well-behaved: for example, a normal Noetherian local ring need not be analytically normal.
The class of excellent rings was defined by Alexander Grothendieck (1965) as a candidate for such a class of well-behaved rings. Quasi-excellent rings are conjectured to be the base rings for which the problem of resolution of singularities can be solved; Heisuke Hironaka (1964) showed this in characteristic 0, but the positive characteristic case is (as of 2016) still a major open problem. Essentially all Noetherian rings that occur naturally in algebraic geometry or number theory are excellent; in fact it is quite hard to construct examples of Noetherian rings that are not excellent.

View More On Wikipedia.org
Recent contents Top users
  1. CorgiDirect

    We have excellent prices and range on BIG WIPES

    Unique, Protection, Tested Shifts PU Foam before it sets from hands, tools and surfaces. No more nasty sticky expanding foam nightmares. Removes all water and oil based coatings before they cure. Banishes stains from cured diamond technology coatings. Quickly removes uncured adhesive residue...
    • CorgiDirect
    • Thread
    • america bigwipes excellent prices range usa
    • Replies: 0
    • Forum: USA
  2. CorgiDirect

    We offer excellent prices on Anton products

    Anton are best known for their popular Sprint Pro range of flue gas analysers, but at CORGI direct we also offer a comprehensive range of pressure & temperature measuring tools and other test equipment, personal CO alarms, gas leak detectors, infra-red thermometers and many more useful tools...
    • CorgiDirect
    • Thread
    • america anton excellent offer prices products usa
    • Replies: 0
    • Forum: USA
  3. CorgiDirect

    Have you seen this excellent price on the Fernox F1 Central Heating Protect 500ml ?

    Have you seen this excellent price on the Fernox F1 Central Heating Protect 500ml ? Only £13.17 ex vat. Check out the full range of Fernox product here - https://corgi-direct.com/fernox-best-prices-online-18160-0000
    • CorgiDirect
    • Thread
    • america central central heating central heating system excellent fernox heating price protect usa
    • Replies: 0
    • Forum: USA
  4. CorgiDirect

    Excellent Prices on Fernox Product

    A leading manufacturer of water treatment chemical products, central heating system filters and plumbing consumables. Excellent Prices on Fernox Product. Take a look today #gasengineers #watertreatment #chemicals https://corgi-direct.com/fernox-best-prices-online-18160-0000
    • CorgiDirect
    • Thread
    • america excellent fernox prices product usa
    • Replies: 0
    • Forum: USA
  5. CorgiDirect

    Excellent Prices on Kamco Powerflush Machines

    Excellent Prices on Kamco Powerflush Machines. Professional, Versatile, Easy to use, highly effective products for flushing heating systems - Get yours today - https://corgi-direct.com/power-flush-machines-18089-0000… #kamco #Powerflush #Heatingsystems
    • CorgiDirect
    • Thread
    • america excellent kamco machines powerflush prices usa
    • Replies: 0
    • Forum: USA
  6. CorgiDirect

    Dickies Workwear - Excellent Prices

    Built for the roughest of days & extreme conditions for the professional engineer VIEW HERE
    • CorgiDirect
    • Thread
    • america dickies excellent prices usa workwear
    • Replies: 0
    • Forum: USA
  7. CorgiDirect

    Testo Flu Gas Analysers From CORGI direct - Excellent Prices

    Testo flue gas analysers cover basic domestic boiler testing, all the way through to the needs of commercial boiler engineers. These multi-functional devices allow heating engineers to test gas pressures, flow and return temperatures VIEW HERE -...
    • CorgiDirect
    • Thread
    • america analysers corgi direct excellent flu gas prices testo usa
    • Replies: 0
    • Forum: USA
  8. CorgiDirect

    Excellent Prices on kane analysers. New range added and available to purchase

    Are you ready for the heating season ? VIEW HERE
  9. CorgiDirect

    CORGI Bronze Pump now available - Excellent Price - Best Online

    VIEW HERE
  10. CorgiDirect

    ADEY, Scalemaster and Fernox Filters Now Available - Excellent Prices

    Adey Magnaclean Professional 2 Chemical Pack Only £72.99 Ex VAT Many more filters in the range VIEW FULL RANGE HERE
  11. CorgiDirect

    Arctic Hayes Pipe Cutters Now on Clearance Sale - Excellent Prices

    BUY HERE
  12. CorgiDirect

    Excellent Prices on Kamco Power Flush Machines

    https://www.corgi-direct.com/kamco-products-17951-0000 …
  13. CorgiDirect

    Honeywell Products Now Available - Excellent Prices

    VIEW HERE
  14. CorgiDirect

    Arctic Personal CO Alarm Only £34.99 ex VAT - Excellent Price

    VIEW HERE
  15. CorgiDirect

    Excellent Price on Hayes 2KW Fan Heater Online Quantity Discounts

    Buy 1-4 £9.49 ex VAT each Buy 5-99 £8.49 ex VAT each Buy 100+ £7.75 ex VAT each VIEW HERE
  16. CorgiDirect

    Excellent Price on Hayes 2KW Fan Heater - Best Price Online - Real Bargain

    Buy 1-4 for £9.49 ex VAT each Buy 5-99 for £8.49 ex VAT each Buy 100+ for £7.75 ex VAT each VIEW HERE
  17. CorgiDirect

    Excellent Prices on CORGI Controls & Valves. Synchron Motor Only £7.08 ex vat

    Excellent Prices on CORGI Controls & Valves. CORGI SYNCHRON MOTOR only £7.08 ex vat CORGI 22MM AUTOMATIC BYPASS VALVE Only £9.92 ex vat. View Range Here
  18. CorgiDirect

    Excellent Prices on CORGI Chemicals. 1LT Inhibitor & Cleansers Only £3.75 ex vat

    Excellent Prices on CORGI Chemicals. CORGI 1LT SYSTEM INHIBITOR only £3.75 ex vat CORGI 1LT SYSTEM CLEANSER only £3.75 ex vat. View the CORGI Chemicals here
  19. M

    Looking for experienced plumbers!! IMMEDIATE START, excellent rates of pay, company vehicle.

    Ultraheat Plumbing & Heating Services Ltd are Hiring!! We are a family run business located in Ferndown, Dorset. We are looking for experienced plumbers to join our busy team. Must have at least 5 years experience, confidence when working, be able to work as a member of a team or on own...
  20. D

    Excellent pipe bending skills

    Come on, Fess up!! Which one of you did this?
Creating content since 2001. Untold Media.

Newest Plumbing Threads

Back
Top
AdBlock Detected

We get it, advertisements are annoying!

Sure, ad-blocking software does a great job at blocking ads, but it also blocks useful features of our website. For the best site experience please disable your AdBlocker.

I've Disabled AdBlock